1. Field of the Invention
This invention generally relates to a compact betatron electron accelerator. More particularly, a single coil drives both a core section and a guide field eliminating a need for, and space occupied by, separate drive coils separated by an air gap.
2. Background of the Invention
Oil well bore hole logging is a process by which properties of earth strata as a function of depth in the bore hole are measured. A geologist reviewing the logging data can determine the depths at which oil containing formations are most likely located. One important piece of the logging data is the density of the earth formation. Most present day well logging relies on gamma-rays obtained from chemical radiation sources to determine the bulk density of the formation surrounding a borehole. These sources pose a radiation hazard and require strict controls to prevent accidental exposure or intentional misuse. In addition, most sources have a long half life and disposal is a significant issue. For some logging applications, in particular determination of formation density, a 137Cs source or a 60Co source is used to irradiate the formation. The intensity and penetrating nature of the radiation allow a rapid, accurate, measurement of the formation density. In view of the problems with chemical radiation sources, it is important that chemical radiation sources be replaced by electronic radiation sources. The main advantage of the latter is that they can be switched off, when no measurement is made and that they have a minimal potential for intentional misuse.
One proposed replacement for chemical gamma-ray sources is a betatron accelerator. In this device, electrons are accelerated on a circular path by a varying magnetic field until being directed onto a target. The interaction of the electrons with the target leads to the emission of Bremsstrahlung and characteristic x-rays of the target material. Before electrons can be accelerated, they are injected into a magnetic field between two circular pole faces at the right time, with correct energy and correct angle. Control over timing, energy and injection angle enables maximizing the number of electrons accepted into a main electron orbit and accelerated.
A typical betatron, as disclosed in U.S. Pat. No. 5,122,662 to Chen et al. has a pole face diameter of about 4.5 inches. The magnet consists of two separated, magnetically isolated pieces: a core with a magnetic circuit that is a nearly closed loop and a guide field magnet that includes two opposing pole faces separated by a gap of about 1 centimeter. The pole faces that encompass the core have a toroidal shape. A gap of about 0.5 cm separates the core from the inner rims of the pole faces. The two pieces are driven by two separated sets of coils connected in parallel: a field coil wound around the outer rims of the pole faces and a core coil wound on a center section of the core. The field magnet and the core are magnetically decoupled with a reverse field coil wound on top of the core coil. Both the core coil and the reverse field coil locate in the 0.5 cm gap. U.S. Pat. No. 5,122,662 is incorporated by reference in its entirety herein.
In operation, a typical betatron satisfies the betatron condition and accelerates electrons to relativistic velocity. The betatron condition is satisfied when:Δφ0=2πr20ΔBy0  (1)where:    r0 is the radius of a betatron orbit located approximately at the center of the pole faces;    Δφ0 is the change of flux enclosed within r0; and    ΔBy0 is the change in guide field at r0.
The betatron condition may be met by adjusting the core coil to guide field coil turn ratio as disclosed in U.S. Pat. No. 5,122,662. Satisfying the betatron condition does not insure the machine will work. Charge trapping, injecting electrons into the betatron orbit at the optimal point of time, is another challenging operation. In the 4.5 inch betatron, this is accomplished by holding the flux in the core constant while increasing the guide field. It can be done because the core and guide field are driven independently.
Large betatrons are suitable for applications where size constraints are not critical, such as to generate x-rays for medical radiation purposes. However, in applications such as oil well bore holes where there are severe size constraints, it is desired to use smaller betatrons, typically with a magnetic field diameter of three inches or less. The conventional design for large betatrons is not readily applied to smaller betatrons for a number of reasons:                (1) If the electron injector is located in the gap between pole faces, the gap height must be larger than the dimension of the injector perpendicular to the pole faces. In order to maintain a reasonable beam aperture, the width of the pole faces can not be reduced too much either. Thus, the burden of the size reduction falls mostly on the core, resulting in a significantly lower beam energy.        (2) If the electron injector is located in the gap between the pole faces, one must, within a time period comparable to the orbit period of electrons, alter the injected electrons trajectories such that they do not hit the injector. Those electrons whose trajectories do not intercept either the injector structure and the vacuum chamber walls are said to be trapped. Only trapped electrons may be accelerated to full energy and caused to impinge on the target and produce radiation. Due to the nature of the charge trapping mechanism, the probability of trapping any charge in a 3 inch machine is almost nil unless the modulation frequency of the main drive is increased to about 24 kHz (triple that of a 4.5 inch machine) and the injection energy is reduced to about 2.5 kV (½ that of the 4.5 inch machine). Even then, the prospect of trapping a charge comparable to that trapped in a 4.5 inch machine is poor.        (3) A higher flux density is required to confine the same energy electrons to a smaller radius. A higher flux density and modulation frequency results in a higher power loss in a three inch betatron, even though it has a smaller volume than a 4.5 inch betatron.        
As a result of (1)-(3), it is estimated that the useable radiation output of a three inch betatron with the conventional design would be three orders of magnitude lower than the 4.5 inch betatron. There exists a need for a small diameter betatron having a radiation output comparable to the 4.5 inch betatron.